Answer:
(a)
(b) $7.44
(c) Yes.
Step-by-step explanation:
The exponential function representing the cost of a movie ticket in a large city is as follows:
(a)
A decade equals 10 years.
Then for <em>n</em> decades the number of years will be,
<em>y</em> = 10 × <em>n</em>
Then the equation of the cost of a movie ticket in terms of <em>y</em> years after 1953 is as follows:
The equation represents the cost of a movie ticket in
(b)
For the year 1953, the value of <em>y </em>is 0.
So, for 1996 the value of <em>y</em> will be, 44.
Compute the cost of a movie ticket in 1996 as follows:
Thus, the cost of a movie ticket in 1996 will be $7.44.
(c)
It is already provided that the cost of a movie ticket in a large city has increased exponentially over the decades since 1953.
So, for the year 1953 the cost of a movie ticket was, $1.25.
And the cost of a movie ticket in 1996 was $7.44.
This value shows an exponential increase in the cost.
Thus, the estimate in part b is reasonable.